Thermal Model of a Thinned-Die Cooling System

Abstract

For through-silicon optical probing of microprocessors, the heat generated by devices with power over 100W must be dissipated [1]. To accommodate optical probing, a seemingly elaborate cooling system that controls the microprocessor temperature from 60 to 100° C for device power up to 150W was designed [2]. The system parameters to achieve the desired thermal debug environment were cooling air temperature and air flow. A mathematical model was developed to determine both device temperature and input power. The 3-D heat equation that governs the temperature distribution was simplified to a case of a 1-D rod with one end at the device center and the other at the cooling air intake. Thus the cooling system was reduced to an analytical expression. From experimental data, we computed all coefficients in the model, then ran extensive tests to verify—the accuracy was better than 10% over the entire temperature and power ranges.